The Pew Research Centre released a study in January 2011 of Muslim population growth world wide (here). The figures for Europe are summarised in the chart below. Downloadable PDF here.

Muslim attitudes to democracy, the rule of law and terrorism:

This section addresses the oft-heard view that there is just “a tiny minority of extremists” in an otherwise moderate, benign and peaceable Muslim congregation. Depends what you mean by moderate and benign, of course, but let’s just take it as being a common-sense understanding: we expect moderates, in any religion, to abide by the laws of the state, to live and let live, to pursue their religion in private and to show tolerance to the views of all in the community.

The statistics do not support the widely-held belief that the vast majority of Muslims are moderate and peaceable in the sense above. Large minorities, in some cases majorities, support terrorist actions and favour imposition of Sharia law.

ICI Research added12 May 2016. More than 100,000 British Muslims support suicide bombers and terrorist acts. 23% of British Muslims say Sharia law should replace UK laws. 52% say homosexuality should be illegal. 39% say women should always obey their husbands. [April 2016 Poll]53% of British Muslims believe Islamic values are “not compatible with British values”. Ref55% of British Muslims either support terrorism or say they want Islamic Sharia law in the UK rather than England’s democratic system. Ref.40% support for Sharia in the UK; 33% want a worldwide Islamic caliphate and the same number believe that killing for Islam is justified; 40% don't think men and women should mix freely; 24% don't think men and women are equal, 25% don't like gays. Ref.

25% of British Muslims believe the July 2005 terror bombings in London “were justified” [that's about 700,000 British muslims]. But...A more conservative estimate is given by the UK Security Service. "Only" 100,000 UK Muslims believe the 7/7 attacks were justified....

“…my officers and the police are working to contend with Some 200 groupings or networks, totalling over 1600 identified individuals (and there will be many we don't know) who are actively engaged in plotting, or facilitating, terrorist acts here and overseas..... This view is shared, in some degree, by a far wider constituency. If the opinion polls conducted in the UK since July 2005 are only broadly accurate, over 100,000 of our citizens consider that the July 2005 attacks in London were justified”.

40% of British Muslims surveyed say they back Sharia law in parts of Britain.ICM Survey, Feb 06.

37% of British Muslims 16-24 want Sharia law (compared with 17% of 55+ year olds. Policy Exchange.31% of British Muslims 16-24 believe Apostasy should be punishable by death (19% for 55+). Policy Exchange.13% of British Muslims 16-24 support Al Qaeda (3% of 55+). Policy Exchange.74% of British Muslims 16-24 want women to wear veil or hijab (28% of 55+). Policy Exchange.> 57% of arrests and > 73% of sentences for terrorism 2001 to 2012 were Muslims. Home Office, 12 Sep 2013.In sum: 37% to 55% of British Muslims want Sharia law in the UK. Large minorities believe the 7/7 suicide-murder attacks were justified. Majorities of terrorism acts were by Muslims.United States:44% of US Muslims surveyed say that those who "criticize or parody Islam in the US should face criminal prosecution". (Wenzel Strategies. Added here 12 March 2013)In the US, 26% of young Muslims support suicide murder in the "defence of Islam". Pew Research Center, July 14, 2005. Ref.

In the US, 40% of Muslims believe they should be judged by Sharia, not US law. WND, 30 October 2012. Ref.Holland (added 19 Dec 2014): 80% of Dutch Muslims support Jihad. [ref] Muslim views in Muslim countries (including Apostasy):Large majorities of Muslims in Muslim countries support the harsh punishments of Sharia Islamic law. For example:

Note: The "Harsh Punishments" mentioned above are mandated by Sharia law. See Undat al-Salik, the Classic Manual of Islamic Jurisprudence. It specifically mandates each of the above penalties.

13.5% of Muslims worldwide, 160 to 200 million, believe the 9/11 attacks were “fully justified”. 36% of Muslims worldwide, 430 to 540 million, think the attacks were “in some way justified”. Total "fully or in some way justified": 50%, 600 to 750 million. Gallup study “Who speaks for Islam? What a Billion Muslims Really Think”. Gallup Research.Ref.[1]

This section addresses the oft-heard complaints by Muslims and non-Muslim apologists that there is a rash of “Islamophobia” in the west, directed with bigotry towards Muslims. The figures on hate crimes in the US – a reasonable statistical proxy for “Islamophobia” – show that the opposite is the case. Hate crimes against Muslims are low and have been declining. Moreover, they are significantly lower than similar crimes against Jews.

UPDATE (18 Dec 2014):

The FBI’s newly released hate crime statistics for 2013 offer a fresh example of how reality refuses to conform to thedubiousnarrative of widespread Muslim victimization at the hands of American bigots. As in previousyears, most hate crimes were not religiously motivated, most religiously motivated hate crimes were anti-Jewish, and Muslims suffered fewer total incidents than many groups and fewer per capita than gays or Jews. Anti-Islamic crimes did not involve greater violence than others and have not become more frequent. A glance at the details.... [source]

To anticipate criticism that the above chart is "racist" or "Islamophobic", or that correlation does not imply causation, I make these points: (i) Islam is not a race. The correlation is between an ideology -- Islam -- and civil & political rights. (ii) The Arab Development Report of 2009 made similar points about the backwardness of the Muslim world. (iii) While correlation does not necessarily mean causation, in this case, the causation is a reasonable hypothesis, supported both by the Arab Development Report and knowledge of the rights-inhibiting nature of the tenets of Islam, its doctrines and practices. In short, supposition of a causation between more Islam and fewer political/civil rights does not do violence to common sense and familiarity with those tenets.Muslim attitudes to homosexuality: 100% of British Muslims think that homosexuality is morally wrong. Guardian poll.Pat Condell: "How Gay is Islam?" YouTube, 11 Nov 2013.

Terrorist organisations:

This section addresses the claim that “all religions have their extremists”, or that “all religions are the same and have a tiny minority who commit terror acts”, and the like.

Mosques in the US:
Five studies -- from 1998 to Summer 2011 -- show close agreement: about 80% of US mosques preach "extremist ideology" or carry extremist publications in their libraries. The detail is here.

European Concerns Over Muslim Immigration Go Mainstream
By Soeren Kern, August 15 2011.
A dozen recent polls from likes of Pew Research and center-left Le Monde newspaper. Summary:

A new opinion survey shows that more than half of all Europeans believe there are too many immigrants in their countries and that immigration is having a negative impact on their lives.

The findings – which come as Europeans are waking up to the consequences of decades of mass immigration from Muslim countries – point to a growing disconnect between European voters and their political masters regarding multicultural policies that encourage Muslim immigrants to remain segregated rather than become integrated into their host nations.

Pew Poll on Attitudes of Muslim Americans
Pew Poll of August 30 2011 shows 21% of American Muslims believe there is a "Great deal or Fair amount" of support for Islamic extremism amongst Muslims in the US. [Here]

Correlation between Child Brides and Islam
There is a 70% correlation between child brides and percentage of Islam. Full report here.

[Last update: 18 Dec 2014, under "Hate crimes against Muslims"]

Pew poll shows around 150 million muslims have "favourable" views of ISIS/IS. Consistent with "What a billion Muslims really think", by Dalia Mogahed and John Esposito", in which the number of Muslims approving of suicide killing of innocent infidels is around 185-210 million.

[Added: 4 April 2016]

ICM Research 13 April 2016: More than 100,000 British Muslims support suicide bombers and terrorist acts. 23% of British Muslims say Sharia law should replace UK laws. 52% say homosexuality should be illegal. 39% say women should always obey their husbands. [Ref]

[1]The Gallup study is immensely flawed, as a critique by Robert Satloff shows. The book based on the study is devoid of any detailed figures, which must be purchased from Gallup for $US 20,000. In response to questions by Satloff at a conference on the study, Mogahed said that the figures would be posted on the Gallup site. That was nearly three years ago, and still nothing.

"...it is the duty of those who have accepted Islam to strive unceasingly to convert or subjugate those who have not. This obligation is without limit of time or space. It must continue until the whole world has either accepted the Islamic faith or submitted to the power of the Islamic state."

-- Bernard Lewis, renowned historian of Islam and the Middle East, in The Political Language of Islam, p72-3.

In other words:

"Islam is unique among religions of the world in having a developed doctrine, theology and legal system that mandates warfare against unbelievers."